Binomial Probability Calculator

Explore the world of probability with our interactive calculator. Understand the likelihood of successes in binomial trials and visualize the distribution.

Trials

Total number of independent experiments.

(0 to 1)

Likelihood of success in a single trial.

Successes

Desired number of successful outcomes.

Calculation Result:

Formula: $$P(X=k) = {n \choose k} \cdot p^k \cdot (1-p)^{n-k}$$
Probability:

Binomial Distribution Visualization:

Understanding Binomial Probability

The Binomial Probability Calculator is designed to help you calculate the probability of achieving a specific number of successes in a series of independent Bernoulli trials. Each trial in a binomial experiment has only two possible outcomes: success or failure. This tool is particularly useful in various fields such as statistics, quality control, and risk assessment.

For example, if you are flipping a coin 10 times and want to know the probability of getting exactly 5 heads, you can use this calculator. Simply input the number of trials (n=10), the probability of success on a single trial (p=0.5 for a fair coin), and the desired number of successes (k=5). The calculator will then compute the binomial probability for you and visualize the distribution.

Key Terms:

  • Number of Trials (n): The total number of independent trials or experiments.
  • Probability of Success (p): The probability of success in a single trial, ranging from 0 to 1.
  • Number of Successes (k): The specific number of successes for which you want to calculate the probability.

Learn more about binomial distribution on Wikipedia.